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Zbl 0555.62010
Rubin, Donald B.
Bayesianly justifiable and relevant frequency calculations for the applied statistician. (English)
[J] Ann. Stat. 12, 1151-1172 (1984). ISSN 0090-5364

The present paper is the revised text of a special invited IMS lecture presented at the joint meeting of the IMS and ASA, August 21, 1982, Cincinnati, Ohio, by the author. It consists of an introduction and six sections. In the introduction the meaning of the terms used in the title of the paper is described. \par Section 2 presents several reasons why the applied statistician should care about Bayesian methods of inference. Section 3 describes simple frequency calculations that are useful in practice for understanding and communicating Bayesian statements, as well as frequency calculations that calibrate Bayesian statements by tying them to frequencies of real-world events. \par Section 4 discusses the use of frequency calculations to examine the operating characteristics of Bayesian inferences in order to guide the choice of models on which to base inferences. Section 5 describes the use of posterior predictive frequency distributions of test statistics to monitor the adequacy of specific model specifications with fixed data sets. Finally, Section 6 concludes with a few summary comments.
[J.Melamed]

MSC 2000:: *62A01 Foundational and philosophical topics
62F15 Bayesian inference
62-07 Data analysis (statistics)
62P99 Appl. of statistics

Keywords: calibration; empirical Bayes; model monitoring; posterior predictive checks; stopping rules; frequency calculations; operating characteristics; posterior predictive frequency distributions; model specifications

Cited in: Zbl 1119.62022 Zbl 1069.62027 Zbl 0820.62027

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